Monday, September 04, 2006

* Chances Are by Michael Kaplan

Don’t bother to read this book, and please just settle for the blogged version I am about to share with you.

The best experiments deduce an effect from the hypothesis and then isolate it in the very context in which it may be disproved. This falsifiability is what makes a hypothesis different from a belief – and science distinct from the other towers of opinion [such as religion]. P7

A taxi sideswipes a car on a winter night. There are 2 taxi companies in town: Blue and Green. The latter owns 85% of the cabs. A witness says she saw a Blue taxi. Independent tests suggests she makes a correct identification 80% of the time. So what color was the taxi? Almost everyone says that it was blue, because people concentrate on the reliability of the witness. But the real issue is how her reliability affects the base fact that a random taxi has an 85% chance of being green. When those 2 probabilities are combined, the chance that the taxi was green is actually 59% - more likely than not. P9-10
The book desperately needed to publish this calculation, and another reason why I can’t recommend it.
20% chance of error and 85% chance of cabs being green; 20%x85%=17% (thus 83% chance of her being right and the car blue or green).
80% chance of being correct and 15% of cabs being blue=12% (thus 88% chance of being right or wrong and the cab green).
80% chance of being correct and 85% of cabs being green,= 68% chance of being correct for green (thus 32% chance of being blue)
20/100 times she’s wrong. 15/100 times the cab is blue, so 3% of the time she’ll call this green. But she told us it was blue, so even if the car was green, she was mistaken. So isn’t the answer so obviously 59% to you?

An experimenter showed people 2 urns. One contained 50% red, and 50% black balls; the other contained an unknown proportion of red and black balls. He offered $100 to any subject ho drew red ball from either urn. Which urn would you choose? Almost all subjects chose the known proportion 50/50 over the unknown. Then you’re offered another $100 to draw a black ball; the same subjects still chose the 50/50 urn – even though their 1st decision suggested that they thought the unknown urn had more black balls and fewer red ones. P11

The Emperor Augustus spent whole days gambling with his cronies. Claudius wrote a book on dice and had his sedan chair rigged for playing on the move. Caligula of course, cheated. Tacitus said “So bold are the German barbarians about winning and losing, that, when they have gambled away all else, they stake their own freedom on the final throw.” P13 Hey, don’t give the Vegas casinos any ideas!

Descartes’ belief that staying in bed until noon was essential to the proper working of his brain has made him the hero of every well-read adolescent. P21

Logarithms ease calculation by considering any large number as a base raised to some power. Instead of trying to multiply large numbers, we can simply add powers of 10 that represent them, since 10^4x10^6=10^10. So if x=10^a, then a=logx. P34

May the force be with the Brits?
The 2001 UK census reveals that 40% of the children are born single mothers… The same census also reveals that 390,000 people state their religion as ‘Jedi’. P112

In a group of 33 clinical trials on death from stroke, with a total of 1066 patients, the treatment being tested reduced mortality on avg from 17.3% in the control group to 12% in the treated group – a reduction of 25%. Are you impressed? Do you want to know what the treatment is? It’s rolling a die [in a simulated experiment]… The rules were simple: rolling a ‘6’ meant the simulated patient would die. Overall mortality averaged out would be 1/6 or 17.5%. But two simulations out of 44 showed statistically significant results. P159

The breakfast of champions or klutzes?
High correlation is not enough for inference: when an effect is naturally rare and the putative cause is very common, the chance of coincidence becomes significant. If you asked people with broken legs whether they had eaten breakfast that morning, you would see a very high correlation. P162

In the 1960s, controls for heart studies had their chests opened and immediately sewn up – a procedure unlikely to pass the ethics committee now… Considerable work has gone into developing placebos that while inactive for the condition being tested, provide side effects associated with the treatment… Also the placebo effect is well documented. If a control group patient improves, it needn’t be because of the placebos; some simply get better… You need, essentially a control for your control- another group you are not even trying to please. “Would you like to participate in a study where we do nothing for your condition?” Might this message affect the patient’s well being? P163

You’re in charge of a mammogram screening program for women between 40 and 50 who show no symptoms. The overall probability that a woman has breast cancer is .8%. If a woman has breast cancer, she has a 90% probability of showing a positive result. If she doesn’t have cancer and she shows a false positive is 7%. A patient has a positive result. What is a probability that she has cancer? [Don’t worry, read on.] Doctors in a German teaching hospital were baffled: 1/3 decided the probability was 90%; 1/6 thought 1%... Phrase the question again this way: out of 1000 women, 8 will have breast cancer. When you screen those 8, 7 will have a positive mammogram. When you screen the remaining 992, 70 of them will have a false positive. Your patient then has only a 10% chance of having cancer! P171

Magic bullet?
Combining folic acid with aspirin in a generic cholesterol and blood pressue lowering drug and giving that to everyone over 55 (assuming the benefits are multiplicative – a big assumption by the way) should cut the risk of heart attacks by 88%, stroke by 80%. Average lifespan could increase by 11 years. P173

Field Marshall Montgomery told the world that ‘there are 3 rules of war. Never invade Russia. Never invade China. Never invade Russia or China.” P240

If you were a Frankish Knight in the 10th century, your view of war would be very different. Your hut is marginally bigger than your neighbors, you are the only one not required to work the land; your business is the protection of those who do. Better fed, better trained, and better armed than any peasant, you lend your invulnerability to the village; it as if, in you, they owned a tank. Your only hope of improving your position is through seizing the cattle or harvest of the neighboring village – but it too owns a knight. But then if it didn’t, your villagers wouldn’t be threatened, and wouldn’t need you. Your most dangerous enemy is also essential justification for your existence… It was only when the Crusades offered the prospect of booty beyond the neighbor’s barns that war became organized again. With that organization and cooperation all could gain more than they had before, came a new concept of knightliness: the code of chivalry, adding to valor the ideals of obedience, loyalty, discipline, and self-restraint. P241

Dollar auction (try this at your next cocktail party!)
Offer to auction a dollar to the highest bidder but with one devilish twist; that the 2nd highest bidder would have to pay their losing bid to you. So if you bid .70, and your neighbor bids .75, he gains a quarter, while you lose .70. Even if you had to buy the dollar for $1.10, at least you’d only lose a dime instead of .70… Bidding will usually slow as you reach the dollar mark, but once past would zoom well beyond it. People will buy a dollar for the average price of $3.40! p256

Lets say that there are 1000 terrorists operating in the US. If we had 99% accurate test of identifying a suspect by sifting through publicly held information, we would end up accusing 2.8 million innocent people (1 in 300,000 of these will be an actual terrorist). And no matter what we do, 10 terrorists would get through, and you only need one whacko… As Ben Franklin said “They that can give up essential liberty to purchase a little temporary safety, deserve neither liberty nor safety.” P273

Boltzmann stated that low entropy can spontaneously arise from high entropy, but low entropy is the same as low probability [and we mean low]… He calculated that the probability that the molecules in a gas in a sphere with a tiny radius of only .00001cm will return to any given configuration is once in 3x10^57 years – some 2x10^47 times the age of the universe so far. P286

No comments: